1. Field of the Invention
This invention pertains generally to a method of optimizing the scheduling of inspections of heat exchanger tubes and minimizing the number of tubes to be sampled as part of that inspection, and more particularly, to the optimization of the inspection of second generation nuclear powered steam generators in a risk informed manner.
2. Related Art
Steam generators in nuclear power reactor systems have a primary side through which the reactor coolant is circulated and a secondary side in heat exchange relationship with the primary side. The reactor coolant enters an inlet plenum and is circulated through tubes to an outlet plenum where it is returned to the reactor. The secondary side includes a water reservoir that surrounds the tubes that is fed by a feedwater inlet. The heat from the primary side converts the water on the secondary side to steam, which is used to drive a turbine that in turn powers a generator to create electricity. The tubes through which the primary coolant passes shield much of the radioactivity carried by the coolant, from the secondary side. The number of such tubes in a typical power plant steam generator can number in the order of thousands. Tube integrity is a safety concern and is therefore monitored. Tube degradation can arise from a number of causes, e.g., corrosion, vibration, etc. Therefore, it has been the practice to periodically inspect the tubes, so that tubes exhibiting a defined degree of degradation can be identified and repaired before being placed back in service. Because of the number of tubes and the environment in which they have to be inspected, the inspection process can be extremely costly.
Second generation nuclear steam generators have been designed to be less susceptible to various modes of tube degradation than their first generation counterparts. Second generation steam generators are found both as original equipment on newer power plants and as replacements for first generation units. The increased resistance of the new generation of steam generators to tube corrosion offers the opportunity for nuclear utilities to consider reducing the frequency and, possibly, the number of tubes inspected. Because steam generator tubing is xe2x80x9csafety significantxe2x80x9d in the sense that challenges to tubing integrity can affect the probability of core damage in the unlikely event of certain postulated accidents, the reduction of inspection sampling currently common for first generation steam generators must be art done in a manner that engenders a high degree of confidence that safety will not be compromised.
A xe2x80x9crisk-informedxe2x80x9d approach offers one potential avenue for reducing the frequency and amount of inservice inspection of second-generation steam generator tubing. The United States Nuclear Regulatory Commission, which has regulatory authority over the subject issue, is committed to a risk-informed approach to reducing the operational costs of achieving acceptable safety levels, e.g., RG 1.174, U.S. Nuclear Regulatory Commission, xe2x80x9cAn Approach Using Probabilistic Risk Assessment in Risk-Informed Decisions On Plant-Specific Changes To The Licensing Basis,xe2x80x9d July 1998. Essentially, the risk-informed approach supplants or augments, usually the latter, traditional deterministic engineering design and structural analysis methods with probabilistic methods. Because risks are explicitly evaluated, there is less need to incorporate conservatism and the result can be a significant reduction in safety-related inspection or testing without impairing safety. In the present case, there is a reason to believe that much of the safety-related inspection thought necessary for first generation tubing is an unnecessary expense for second generation tubing. Risk-informed methods can potentially be applied to determine just how far a specific nuclear plant can go in reducing these costly inspections while maintaining or, possibly enhancing, acceptable safety.
Current steam generator tube integrity guidelines, NEI 97-06, Revision 1B (Draft), xe2x80x9cSteam Generator Program Guidelines,xe2x80x9d Nuclear Energy Institute, Washington, D.C. (April 2000) and EPRI TR-107621-R1, Electric Power Research Institute, xe2x80x9cSteam Generator Integrity Assessment Guidelines: Revision 1xe2x80x9d, March 2000, call for performing a condition monitoring evaluation at each steam generator inspection. This is described as a backward-looking analysis of the inspection results. The primary objective of the condition monitoring analysis is to establish that the most limiting inspected steam generator tubes do not violate a structural limit based on xe2x80x9c. . . a minimum burst pressure of 3 times the normal operating pressurexe2x80x9d that is determined through engineering analysis. Tangible outputs of the condition monitoring analysis include the aforementioned structural limit expressed as a fraction or percent of the tube wall thickness and, typically, a set of statisticsxe2x80x94the mean and standard deviationxe2x80x94on the xe2x80x9cthroughwallxe2x80x9d growth rates per effective full power year (EFPY),xe2x80x9d and a frequency distribution on the depths of all indications found. EFPY is the time period over which the steam generator saw service that equals the amount of full service the steam generator would have experienced if it was operated continuously over a full year.
Sampling protocols for inspections differ substantially in practice but the Electric Power Research Institute (EPRI) Pressurized Water Reactor Steam Generator Inspection Guidelines, EPRI TR-107569-VIR5, Electric Power Research Institute (EPRI), xe2x80x9cPWR Steam Generator Examination Guidelines,xe2x80x9d Rev 5, Vol. 1, September 1997, can be taken as representative of the current state of the art. The EPRI inspection guidelines recommend a xe2x80x9ctriple sample plan,xe2x80x9d which to the extent pertinent, can be summarized as follows:
(1) Take a sample of 20% of the tubes in a steam generator and inspect for degraded tubes, where the latter are tubes where the maximum indication of a degradation falls between some minimum threshold depth, nominally 20%, and the maximum depth beyond which the tube must be repaired, nominally 40%. A degradation beyond 40% of the tube""s through-wall thickness is required to be repaired before the tube can placed back in service.
(2) xe2x80x9cAcceptxe2x80x9d, i.e., stop sampling, the tubes if the fraction of tubes found to be degraded falls below a minimum criterion of 5%. If the fraction found degraded falls between the minimum and maximum criteria, i.e., 5%-10%, then take a second sample of 20% of the tubes. xe2x80x9cRejectxe2x80x9d the steam generator tubes, i.e., sample 100% the steam generator tubes, if the fraction of the sample found to be degraded exceeds a maximum criterion of 10% of the tubes.
(3) Cumulate the fraction found degraded in the first and second samples and utilize the same minimum and maximum criterion and decision rule on the second sample. If the cumulative degraded number of tubes fall between minimum and maximum criterion, then take a third and final sample of an additional 20% of the tubes.
(4) If the cumulative fraction degraded is less than or equal to five percent of the total tubes sampled, then accept the inspection as being complete. Otherwise, inspect all the remaining tubes of that steam generator. Further, if at anytime the steam generator""s tube lot, i.e., all the tubes in the steam generator that are inspected, is rejected, open another steam generator not originally scheduled for inspection and repeat the above sampling plan on this additional steam generator.
In a typical four-loop plant, i.e., a plant with four steam generators, two steam generators come up for inspection every refueling outage, for example, approximately every 18 months.
The steam generator integrity assessment guidelines, cited above, also call for an xe2x80x9coperational assessment,xe2x80x9d described as a forward-looking analysis whose primary objective is to determine that the aforementioned structural limit will not be exceeded before the next scheduled inspection. The recommended approach of the EPRI Risk Informed Inspection document, EPRI TR-114736-V1, Electric Power Research Institute, xe2x80x9cRisk Informed Inspection for Steam Generators,xe2x80x9d Vol. 1, February, 2000, is to take into account all of the uncertainties in the dispersion of indication depths and measurement errors, and also account for the outer extremes of measured growth rates in indications, i.e., degradations. In essence, this amounts to showing:
1. that the application of the 95th percentile crack growth rate, i.e., the crack growth rate at which 95% of the growth cracks grow at or below, to the largest crack left in service (measured in a most conservative way to incorporate safety margins for analytical and measurement error) will still not produce a crack that will exceed a structurally limiting value before the next contemplated inspection, or equivalently,
2. that the time to exceeding the structurally limiting value (referred to more precisely as an xe2x80x9coperational assessmentxe2x80x9d limit) will be greater than the margin between the structurally limiting and the worst degraded tube left in service divided by the highest plausible crack growth rate.
The term xe2x80x9cstructural limitxe2x80x9d is not used in the preceding description because it has a specific meaning in the nuclear industry with respect to the integrity of steam generator tubes. It is the measured degradation value, e.g., depth, which meets regulatory structural integrity criteria based on using a mean relationship between the burst pressure and the measured parameter, mean material properties, and assuming no uncertainty in the measurement of the structural parameter.
Neither the steam generator tube integrity guidelines, identified previously, nor practice rules out the more probabilistic approach to defining a steam generator tube inspection plan. Specific applications of probabilistic analyses exist for specific modes of degradation. For example, Keating, R. F., Westinghouse report (WCAP14277), xe2x80x9cSLB Leak Rate and Tube Burst Probability and Analysis Methods for ODSCC at TSP Intersections,xe2x80x9d January 1995, uses probabilistic methods to project leak rates and tube burst probabilities for tubes with outer diameter stress corrosion cracking at tube support plates. Further, the Nuclear Regulatory Commission has published draft guidelines, DG-1074, US Nuclear Regulatory Commission, xe2x80x9cSteam Generator Tube Integrity (Draft Guide)xe2x80x9d, December 1998, with explicit probability targets for burst rates. Current practice, however, is fundamentally deterministic and does not employ any probabilistic methods to consider the likelihood of achieving safety targets for stipulated intervals between inspections. The current methods that are employed instead rely on traditional deterministic conservative safety margins. In fact, it may not always be conservative. The practice of assuming that the largest crack will necessarily fail first is questionable, particularly when a large number of tubes have indications of degradation that are just slightly below the limiting tube indication. A probabilistic approach can improve safety or at least increase confidence while providing economic savings by establishing a defensible probabilistic case for reducing the frequency and extent of inspections for second generation steam generators.
Further, the current recommended sampling plan may or may not provide sufficient confidence for a specific plant. The plan is not tied to a specific plant reliability target and not integrated with the results of the condition monitoring activity. It is well-known from acceptance sampling literature that any number of combinations of sample sizes and acceptance criteria (as well as other aspects of a sample plan) may achieve the same reliability at the same confidence and hence, there can exist significant savings from tailoring sampling plans for particular plants that have smaller expected sampling requirements and/or less risk of having to extend an outage by opening a new steam generator to inspection.
Accordingly, it is an object of this invention to provide an improved steam generator inspection plan that provides an economic optimization of scheduled inspections consistent with regulatory reliability targets. It is a further object of this invention, as part of the economic optimization of scheduled inspections, to determine the maximum number of degraded tubes to be left in service and still achieve the reliability targets. Still another object of this invention is to identify the minimum number of tubes to be inspected that are required to demonstrate a stipulated confidence in not exceeding the aforementioned maximum number of degraded tubes that are to be left in service.
These and other objects of this invention are achieved by a method for optimizing the inspection of a heat exchanger including the steps of (a) inspecting a number of tubes in a bundle of the heat exchanger for indications of degradation; and (b) determining the maximum time of service between tube inspections the heat exchanger can operate consistent with the number of degraded tubes left unrepaired at a last inspection, employing a probabilistic algorithm. In the preferred embodiment, the probabilistic algorithm is based upon the extreme value probability distribution theory. In an additional embodiment, the method of this invention determines the minimum number of tubes that need to be inspected to establish that no more than the determined maximum number of degraded tubes will be permitted to remain in service for the contemplated interval of time, employing probabilistic theorems. In the method of this invention, the contemplated interval of time can be a variable selected to minimize the frequency of inspection of the heat exchanger. In the preferred embodiment, the probabilistic theorem employed to determine the minimum number of tubes that need to be inspected is a Bayesian Acceptance Sampling algorithm. In addition, the determining step preferably takes into account the probability of detection of a given one of the degraded tubes.